Problem: Recently you have bought a snow walking robot and brought it home. Suppose your home is a cell (0, 0) on an infinite grid.

You also have the sequence of instructions of this robot. It is written as the string s consisting of characters 'L', 'R', 'U' and 'D'. If the robot is in the cell (x, y) right now, he can move to one of the adjacent cells (depending on the current instruction).

  * If the current instruction is 'L', then the robot can move to the left to (x - 1, y); 
  * if the current instruction is 'R', then the robot can move to the right to (x + 1, y); 
  * if the current instruction is 'U', then the robot can move to the top to (x, y + 1); 
  * if the current instruction is 'D', then the robot can move to the bottom to (x, y - 1). 



You've noticed the warning on the last page of the manual: if the robot visits some cell (except (0, 0)) twice then it breaks.

So the sequence of instructions is valid if the robot starts in the cell (0, 0), performs the given instructions, visits no cell other than (0, 0) two or more times and ends the path in the cell (0, 0). Also cell (0, 0) should be visited at most two times: at the beginning and at the end (if the path is empty then it is visited only once). For example, the following sequences of instructions are considered valid: "UD", "RL", "UUURULLDDDDLDDRRUU", and the following are considered invalid: "U" (the endpoint is not (0, 0)) and "UUDD" (the cell (0, 1) is visited twice).

The initial sequence of instructions, however, might be not valid. You don't want your robot to break so you decided to reprogram it in the following way: you will remove some (possibly, all or none) instructions from the initial sequence of instructions, then rearrange the remaining instructions as you wish and turn on your robot to move. 

Your task is to remove as few instructions from the initial sequence as possible and rearrange the remaining ones so that the sequence is valid. Report the valid sequence of the maximum length you can obtain.

Note that you can choose any order of remaining instructions (you don't need to minimize the number of swaps or any other similar metric).

You have to answer q independent test cases.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 2 ⋅ 10^4) — the number of test cases.

The next q lines contain test cases. The i-th test case is given as the string s consisting of at least 1 and no more than 10^5 characters 'L', 'R', 'U' and 'D' — the initial sequence of instructions.

It is guaranteed that the sum of |s| (where |s| is the length of s) does not exceed 10^5 over all test cases (∑ |s| ≤ 10^5).

Output

For each test case print the answer on it. In the first line print the maximum number of remaining instructions. In the second line print the valid sequence of remaining instructions t the robot has to perform. The moves are performed from left to right in the order of the printed sequence. If there are several answers, you can print any. If the answer is 0, you are allowed to print an empty line (but you can don't print it).

Example

Input


6
LRU
DURLDRUDRULRDURDDL
LRUDDLRUDRUL
LLLLRRRR
URDUR
LLL


Output


2
LR
14
RUURDDDDLLLUUR
12
ULDDDRRRUULL
2
LR
2
UD
0

Note

There are only two possible answers in the first test case: "LR" and "RL".

The picture corresponding to the second test case:

<image> Note that the direction of traverse does not matter 

Another correct answer to the third test case: "URDDLLLUURDR".

Solution (in JAVA):

Solution:
import java.io.DataInputStream; 
import java.io.FileInputStream; 
import java.io.IOException; 
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.io.BufferedReader; 
import java.util.*;



public class C{
	public static FastReader fs = new FastReader();
	
	static PrintWriter out = new PrintWriter(System.out);
	
	static void solve() {
		StringBuffer output = new StringBuffer();
		char s [] = fs.next().toCharArray();
		int moves [] = new int [4];
		for(int i = 0; i<s.length; i++) {
			if(s[i] == 'L')moves[0] += 1;
			if(s[i] == 'R')moves[1] += 1;
			if(s[i] == 'U')moves[2] += 1;
			if(s[i] == 'D')moves[3] += 1;
		}
		if(min(moves[0],moves[1]) == 0 && min(moves[2],moves[3]) == 0) output.append("");
		else if(min(moves[0],moves[1]) == 0)output.append("UD");
		else if(min(moves[2],moves[3]) == 0)output.append("LR");
		else {
			for(int i = 0; i<min(moves[0],moves[1]); i++)output.append('R');
			for(int i = 0; i<min(moves[2],moves[3]); i++)output.append('U');
			for(int i = 0; i<min(moves[0],moves[1]); i++)output.append('L');
			for(int i = 0; i<min(moves[2],moves[3]); i++)output.append('D');
		}
		out.println(output.length());
		if(output.length() != 0)out.println(output);
	}
	
	public static void main(String[] args) {
		int t = 1;
		t = fs.nextInt();
		for(int cs = 1; cs <= t; cs++) {
			solve();
		}
		out.close();
	}
	
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
	
	static int ceil(int x,int y) {
		return (x % y == 0 ? x / y : (x / y +1));
	}
	
	static long ceil(long x,long y) {
		return (x % y == 0 ? x / y : (x / y +1));
	}
	
	static int max(int x,int y) {
		return Math.max(x, y);
	}
	
	static int min(int x,int y) {
		return Math.min(x, y);
	}
	
	static long max(long x,long y) {
		return Math.max(x, y);
	}
	
	static long min(long x,long y) {
		return Math.min(x, y);
	}
	
	static int min(int a []) {
		int x = 1_000_000_00_9;
		for(int i = 0; i<a.length; i++)x = min(x,a[i]);
		return x;
	}
	
	static int max(int a []) {
		int x = -1_000_000_00_9;
		for(int i = 0; i<a.length; i++)x = max(x,a[i]);
		return x;
	}
	
	static long min(long a []) {
		long x = (long)3e18;
		for(int i = 0; i<a.length; i++)x = min(x,a[i]);
		return x;
	}
	
	static long max(long a []) {
		long x = -(long)3e18;
		for(int i = 0; i<a.length; i++)x = max(x,a[i]);
		return x;
	}
	
	static int power(int x,int y) {
		int res = 1;
		while(y > 0) {
			if( y % 2 == 1)res = (res * x);
			y >>= 1;
            x = (x * x);
		}
		return res;
	}
	
	static long power(long x,long y) {
		long res = 1;
		while(y > 0) {
			if( y % 2 == 1)res = (res * x);
			y >>= 1;
            x = (x * x);
		}
		return res;
	}
	
	static long power(long x,long y,long mod) {
		long res = 1;
		x %= mod;
		while(y > 0) {
			if( y % 2 == 1)res = (res * x) % mod;
			y >>= 1;
            x = (x * x) % mod;
		}
		return res;
	}
	
	static void intsort(int [] a) {
		List<Integer> temp = new ArrayList<Integer>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void longsort(long [] a) {
		List<Long> temp = new ArrayList<Long>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void reverseintsort(int [] a) {
		List<Integer> temp = new ArrayList<Integer>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		Collections.reverseOrder();
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void reverselongsort(long [] a) {
		List<Long> temp = new ArrayList<Long>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		Collections.reverseOrder();
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void intpairsort(intpair [] a) {
		List<intpair> temp = new ArrayList<intpair>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp,(p1,p2) -> {
			if(p1.x == p2.x) return p1.y >= p2.y ? -1 : 1;
			else return p1.x > p2.x ? -1 : 1;
		});
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void longpairsort(longpair [] a) {
		List<longpair> temp = new ArrayList<longpair>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp,(p1,p2) -> {
			if(p1.x == p2.x) return p1.y >= p2.y ? -1 : 1;
			else return p1.x > p2.x ? -1 : 1;
		});
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static class intpair{
		public int x;
		public int y;
		
		intpair(int a,int b){
			this.x = a;
			this.y = b;
		}
		
		intpair(){}
	}
	
	static class longpair{
		public long x;
		public long y;
		
		longpair(long a,long b){
			this.x = a;
			this.y = b;
		}
		
		longpair(){}
	}
	
	static class data{
		public long sum;
		
		data(long val){
		    this.sum = val;
		}
		
		data(){}
		
		data combine(data l, data r) {
		    data res = new data();
		    res.sum = l.sum + r.sum;
		    return res;
		}
	}
	
	static class Seg_Tree extends data{
		public int n;
		data [] seg;
		
		Seg_Tree(int sz){
			this.n = sz;
			seg = new data[4*n+4];
		}
		
		void build(long a[], int v, int tl, int tr) {
		    if (tl == tr) {
		        seg[v] = new data(a[tl]);
		    } else {
		        int tm = (tl + tr) / 2;
		        build(a, v*2, tl, tm);
		        build(a, v*2+1, tm+1, tr);
		        seg[v] = combine(seg[v*2],seg[v*2+1]);
		    }
		}

		void update(int v, int tl, int tr, int pos, long new_val) {
		    if (tl == tr) {
		        seg[v] = new data(new_val);
		    } else {
		        int tm = (tl + tr) / 2;
		        if (pos <= tm)
		            update(v*2, tl, tm, pos, new_val);
		        else
		            update(v*2+1, tm+1, tr, pos, new_val);
		        seg[v] = combine(seg[v*2],seg[v*2+1]);
		    }
		}
		
		data query(int v, int tl, int tr, int l, int r) {
		    if (l > r) 
		        return new data(0);
		    if (l == tl && r == tr) 
		        return seg[v];
		    int tm = (tl + tr) / 2;
		    return combine(query(v*2, tl, tm, l, min(r, tm)),query(v*2+1, tm+1, tr, max(l, tm+1), r));
		}
	}
	
	static class Bit_Tree{
		static int n;
		static int [] bit;
		
		Bit_Tree(int sz){
			Bit_Tree.n = sz;
			Bit_Tree.bit = new int[n+1];
		}
		
		static int child(int x) {
			return x + (x & (-x));
		}
		
		static int parent(int x) {
			return x - (x & (-x));
		}
		
		static void build(int [] a) {
			for(int i = 0; i<a.length; i++) {
				int start = i+1;
				while(start <= n) {
					bit[start] += a[i];
					start = child(start);
				}
			}
		}
		
		static void update(int idx,int new_val) {
			idx += 1;
			while(idx <= n) {
				bit[idx] += new_val;
				idx = child(idx);
			}
		}
		
		static int query(int right) {
			int res = 0;
			while(right > 0) {
				res += bit[right];
				right = parent(right);
			}
			return res;
		}
		
		static int query(int left,int right) {
			return query(right) - query(left-1);
		}
	}
}